by Markus Rost (Preprint, August 2000, December 2008, 19 pages)
In these notes we show that the essential dimension of PGL_{4} is equal to 5.
Along the way we discuss (in a rather unsystematic manner) generalities on essential dimension and degree formulas.
Full text (version of December 13, 2008): [dvi] [dvi.gz] [pdf] [ps] [ps.gz]
Update December 2008:
by Markus Rost (Notes, March 2002, 3 pages)
In this note we compute the essential dimension of a Galois module which is cyclic of order 4 (in characteristic different from 2).
Update: The text has been incorporated (in greater detail) as Theorem XII.37.2 in the book
Full text (version of March 2, 2002): [dvi] [dvi.gz] [pdf] [pdf.gz] [ps] [ps.gz]
by Markus Rost (Notes, January 2017, 4 pages)
In this note we describe the cohomological invariants (mod 2) for a Galois module which is cyclic of order 4 (in characteristic different from 2).
Full text (version of January 15, 2017): [pdf]